Permanentmagnet-Synchron-Maschinen Grundlagen des · PDF fileSeminar Prof. Dr.-Ing. habil. ......

FB 18 • Elektrotechnik undInformationstechnik

TECHNISCHE UNIVERSITÄTDARMSTADT

Institut für Elektrische EnergiewandlungProf. A. Binder

PermanentmagnetPermanentmagnet--SynchronSynchron--MaschinenMaschinen

GrundlagenGrundlagen des des BetriebsBetriebs und und derder AuslegungAuslegung

Seminar

Prof. Dr.-Ing. habil. Dr. h.c. Andreas Binder

Institut für Elektrische EnergiewandlungTechnische Universität Darmstadt

Landgraf-Georg-Strasse 4D-64283 Darmstadt

Tel. ++49 (0) 6151 16 24181/[email protected]




Inhalt des Seminars

• 1. Auslegung der Permanentmagnet-Synchronmaschine

• 2. Ansteuerung von PM-Maschinen

• 3. Feldschwächung von PM-Maschinen

• 4. Reluktanzmomente




1. Auslegung der Permanentmagnet-Synchronmaschine




Typischer Querschnitt einer PM-Synchronmaschinemit Oberflächenmagneten

6 Pole, 36 Ständernuten, verteilte 3-strängige Einschicht-Drehstromwicklung, q = 2 Ganzlochwicklung, Ständernuten um eine Nutteilung geschrägt, NdFeB-Magnete unterteilt, 100% Polbedeckung, Niederspannungsrunddraht-Wicklung 400 V, Sternschaltung




AMPERE´s law: Excitation of magnetic field by electric current

The integration of magnetic field strength H along closed loop (curve C), which spans the area A, is equal to the resulting current flow (Ampere turns ) penetrating through the area A.

Positive field direction is connected to positive current flow direction by RIGHT HAND RULE.

sdHC

Example:

Two different currents I1, I2 with two different numbers of turns 1 and N and two different flow directions:

Ampere turns : = N I1 - I2




Verteilte Wicklung - ein Strang erregt (hier: q = 3)

QC

leftrightsrFerFesFesFe HHsHsHsdH ,,,,,,

Electric machine:

Unslotted rotor

Air gap

Slotted stator:

Inserted coils with two coil sides each, where coil current i flows

Ampere´s law for air gap field:

Infinite iron permeability Fe assumed:

Magnetomotive force distribution in air gap: V(x)

Magnetic field strength distribution in air gap: H(x)

Magnetic flux density distribution in air gap: B(x)

)()(,, xxVHHsdH QC

leftright

HV /0VB




Stator-Wanderfeld: 3-phasiges Sinusstrom-system speist die verteilte Wicklung

Field curve moves with increasing time t to the left !

After time T the field curve has passed the distance 2p

Velocity of linear movement is called

pp

syn fT

v

22

synchronous velocity !

Synchronous rotational speed nsynin case of rotating field arrangement:

pf

pv

dv

np

syn

si

synsynsyn

2/2/

2

pfnsyn




Permanent magnet technologyPermanent magnets:- AlNiCo,- Ba-Ferrite and Sr-Ferrite,- Rare earth magnets SmCo and NdFeB

Magnetic field inside permanent magnet:

J: magnetic polarization

Saturated values: Subscript s

Remanence flux density: BR = JRCoercive field strength: HCJ and HCB

JHB 0




Permanent magnet properties

a) b)

B(H)-characteristics:a) (1) Soft magnetic material, (2) PM magnet, b) PM magnets: Second quadrant at 20°C; (1) Al-Ni-Co, (2): Ba-Ferrit, (3): Sm2Co17 (max = 350°C) (4): NdFeB (max = 180°C)




Design of magnet dimensions

Magnet field at no-load: No electric current in stator winding !

Ampere´s law:

Flux continuity:

Surface mounted magnets: , hence:

0)(2 MMC

hHHsdH

ABAB MM

AAM BBM

MMM BHhHB

00Operation of magnets in 2nd quadrant:




Operation of magnets in 2nd quadrant of B(H)-plane

Reversible demagnetization of permanent Irreversible demagnetization ofmagnet by air gap. The operating region of the magnet permanent magnet a) by increased air gap 1 < 2is the second quadrant. With increased temperature the b) by external opposite field - /hM, reaching an remanence and coercive field is decreasing, yielding operating point P2 below the "knee" of the reduced air gap flux density according to operation hysteresis loop.points P1 to P4.




Comparison of different magnetic material for the same flux and demagnetization limit

at 20°C AlNiCo NdFeB, A NdFeB, B Sm2Co17 Ba-ferrite rubber ferriteBR / T 1.3 1.4 1.2 0.95 0.4 0.24

HCB / kA/m 90 1100 900 710 270 175AM/A0 1 0.93 1.08 1.36 3.25 5.4hM/h0 1 0.08 0.1 0.13 0.33 0.51VM/V0 1 0.076 0.11 0.18 1.08 2.8

Rare earth magnets allow for the same flux and the same demagnetization limit a much smaller magnetic volume of only about 10%, which yields compact PM motors, but it is expensive.




Torque generation in PM machines with surface mounted magnets

a) b)

No-load air gap magnetic flux density a) with pole coverage ratio e = 1, and b) with e < 1

Tangential Lorentz-force per conductor

Current flow in stator coils produces with rotor PM air gap field a tangential force on rotor.

Force gives torque !2/sie dFM




How to get maximum force resp. torque for given current amplitude ?

Stator air gap field Bs must be perpendicular to rotor PM field Bp to get maximum torque. The ALL phase currents have the same polarity under one pole and give there fore the SAME force direction. This is like in DC machines = brushless DC Drive system !

Stator field is directed into gaps between rotor magnetic poles (rotor q-axis) = q-axis current operation !

By rotor position sensor the stator currents are switched with inverter to get the right phase shift for q-current operation !

An inverter is needed !




Air gap magnetic flux density for one pole under load

xh

AH

xAhHsdH

Ms

MsC

,

, 2)(2

p

ssp p

INmA

22/

„Current layer“ (loading):

Ampere´s law gives stator field:

Under load surface mounted rotor magnets experience danger of demagnetization at the trailing pole edge, especially when magnet is hot (typically 150 °C).




Block current feeding

a) b)

a) Cross section of PM synchronous machine with 100% pole coverage ratio

b) Trapezoidal no-load stator phase voltage (back EMF); block shaped currentimpressed in phase with back EMF




Torque generation with block current feeding, calculated via internal power

Torque generation with block current feeding, calculated via internal power.

Air gap power:

Electromagnetic torque:

A smooth torque without any ripple is theoretically produced with contribution of two phases at each moment.

esyn MnP 2

)()()()()()()( titutitutitutp WpWVpVUpU

nIU

M pe

2

ˆˆ2




Torque generation with sine wave current feedingSinusoidal phase current is impressed by inverter in phase with sinusoidal back EMF, resulting in

a) pulsating power per phase, but

b) smooth constant power and constant torque for all three phases.

Using internal power per phase we get

constant resulting power:)3/4cos(ˆ)3/4cos(ˆ)3/2cos(ˆ)3/2cos(ˆ)cos(ˆ)cos(ˆ)( tItUtItUtItUtp ppp

1)

382cos(

2

ˆˆ1)

342cos(

2

ˆˆ1)2cos(

2

ˆˆ)( t

IUt

IUt

IUtp ppp

.2

ˆˆ)( const

IUmtp p

nIU

M pe

2

ˆˆ)2/3(




Induced no-load voltage (”back EMF”) in one coil at 100% pole coverage ratio

a) b)

a) Rectangular air gap flux density distribution = 100% pole coverage ratio leads to

b) triangular coil flux linkage time function, causing rectangular shaped induced coilvoltage ui,c = -dc/dt




Back EMF in coil group with q >1 coils

a) Unskewed coils:The induced back EMF is step-like, when being induced by rectangular air gap flux density distribution !

Coil skew: bschr or bsk

Example: q = 2

b) Coils skewed by one slot pitch yield a trapezoidal back EMF




Example: Coil group with q = 3 coils

Unskewed coils:The induced back EMF is step-like !

Coils - skewed by one slot pitch - yield a trapezoidal back EMF !

100 % pole coverage ratio, 3 slots per pole and phase




Influence of pole coverage ratio e on the rotor flux density amplitudes

Rotor air gap field amplitudes:

At e = 0.85 the fundamental amplitude is reduced by 3%, but 5th and 7th harmonic are reduced drastically.

)2/sin(4,

eBB




How to get sinusoidal induced back EMF from NON-sinusoidal rotor air gap field ?

Use of pitched coils:(= two-layer winding needed!)

Flux linkage of pitched coil:

2/

2/, )cos()

2sin(2),()(

W

W pFe

pcFecc tWBlNdxtxBlNt

)2

sin(

p

pWkPitch factor:

1 3 5 7 9 11 13

kp 0.966 -0.707 0.259 0.259 -0.707 0.966 0.966

Reduction of coil flux linkage due to chording W /p = 5/6.




Coil groups help to get sinusoidal voltage !Three-phase winding, 9 slots per pole, q = 3 coils per pole and phase.

209/1809/)/(1 pQQQ

Example:

mqq

m

q

q

UqU

kQ

Q

ci

grid

2sin

2sin

2sin2

2sin2

ˆˆ

,

,

,,

,,,

Distribution factor:

1 3 5 7 9 11 13

kd 0.960 0.667 0.218 -0.177 -0.333 -0.177 0.218Reduction of coil flux linkage due to coil group arrangement q = 3.




Star connected three phase winding suppresses 3rd

harmonic line-to-line voltages and 3rd phase currentsHarmonic induced voltage:

)sin()sin(2)( tUtBlkNtu iFep

wsi

)()3cos())3/4(3cos()()()3cos())3/2(3cos()(

)3cos()(

3333

3333

33

tutUtUtututUtUtu

tUtu

UW

UV

U

If the stator winding is star connected, the third harmonic voltages in all three phases U, V, W are IN phase and IDENTICAL:

Therefore the line-to-line voltages show NO 3rd harmonic component:0)()()()()( 33333 tututututu UUVUUV

003/ 33333333 IIIIIZUI WVU




Skewing helps to suppress slot harmonic back EMFSkewing by the distance bsk reduces flux linkage and therefore induced voltage further by the so-called skewing factor

p

skbSSS

2/)sin(

Example: Six pole machine, rotor speed 1500/min, 5/6 chorded coils, q = 2, 85% pole coverage ratio, magnets skewed by one stator slot pitch

OrdinalNumber

Statorfrequency

Fluxdensity

WindingFactor

Skewingfactor

Inducedphase

voltage

Inducedline-linevoltage

f B kw skew, Ui Ui,LL

1 75 Hz 100 % 0.933 0.989 100 % 100 %3 225 Hz -26.1 % 0.50 0.900 12.7 % 05 375 Hz 7.9 % 0.068 0.738 0.37 % 0.37 %7 525 Hz 1.2 % 0.068 0.527 0.04 % 0.04 %9 675 Hz -5.8 % 0.50 0.300 0.88 % 0

11 825 Hz 7.8 % 0.933 0.090 0.67 % 0.67 %




Auslegungsrichtlinien für PM-Motoren Bemessungsgrössen: Strombelag A, Flussdichte B, Stromdichte J

Läufer-/mittlerer Lagerdurchmesser d/ dm, Läuferlänge lFe

Leistung: P ~ d2lFe.A.B.n

Wicklungserwärmung (Stromwärme): ~ A.J (Einfluss Kühlung)ABER: Ummagnetisierungsverluste PFe ~ B2.nx, x = ca. 1.8

Reibungsverluste PR ~ d.lFe.ny, y = 2 ... 3

Zusatzverluste Pad ~ I2.nz, z = ca. 1.5 ... 2

Mechan. Spannung durch Fliehkraft: ~ vu2, vu = d..n (Umfangsgeschwindig.)

Mechanische Steifigkeit: fe ~ d/lFe2 (Läufer-Biegeeigenfrequenz)

Lagerung: Spezial-Kugellager vm = dm..n ~ dm

.n

Sonderkühlung / Abmessungsgrenzen / Sonderkonstruktion für Festigkeit




Utilization of electrical machinesElectromagnetic utilization C (”Esson´s number”) of electric machines is (inner) apparent machine power S versus speed and ”bore volume” (factor /4 neglected in that definition)

FesildnSC 2

)/(

BAkC w 2

2

For raising power output of a given motor, either speed can be raised or current load and flux density.Due to iron saturation the air gap flux density B amplitude cannot be raised much above 1 T.

Current loading A can be increased by increasing the current (or the number of conductors), but this also means increased losses in the stator. Therefore high current loading is only possible for intensive cooling.




“Power from speed” - “Torque from size”Low speed machines:a) Totally enclosed PM servo motor with self cooling (without any fan):

40.5 Nm, 1000/min, A = 145 A/cm, B = 0.65 T, dsi = 154 mm, lFe = 175 mm, kw = 0.933, C = 1.0 kVAmin/m3, P = 4.24 kW

b) High torque PM motor with water jacket cooling: 737 Nm, 600/min, A = 611 A/cm, B = 0.8 T, dsi = 280 mm, lFe = 200 mm, kw = 0.866, C = 4.9 kVAmin/m3, P = 46.32 kW

High speed machine: PM motor with water jacket cooling: 12 Nm, 24000/min, A = 225 A/cm, B = 0.7 Tdsi = 90 mm, lFe = 90 mm, kw = 0.933, C = 1.7 kVAmin/m3, P = 30.0 kW

Facit:With only 70% higher electromagnetic utilization C the motor c) has about 7

times higher output power than motor a), as speed is increased by factor 24.

Permanentmagnet-Synchron-Maschinen Grundlagen des · PDF fileSeminar Prof. Dr.-Ing. habil. ......

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